Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20287817 | C2 | semidirect |
| 3. #20276431 | C2 | semidirect |
| 4. #20274758 | C2 | semidirect |
| 5. #20272817 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#2140 | C2 | semidirect |
| 14. #16810873 | C4 | semidirect |
| 43. C2×#11719908 | D4 | semidirect |
| 62. C2×C16×C53 | D4 | semidirect |
| 167. #2140 | D53 | semidirect |
| 195. C53 | #13074 | semidirect |
| 226. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284359 | 2 |
| #20276431 | 2 |
| #20274758 | 2 |
| #20272817 | 2 |
| #20272816 | 2 |
| C53×#2140 | 2 |
| #13074 | 53 |